1、(20%) A vendor of milk products produces and sells low-fat dry milk to a company that uses it to produce baby formula. In order to determine the fat content of the milk, both the company and the vendor take a sample from each lot and test it for fat content in percent. Ten sets of paired test results | Lot Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Company Test Results (X) | 0.50 | 0.58 | 0.90 | 1.17 | 1.14 | 1.25 | 0.75 | 1.22 | 0.74 | 0.80 | | Vendor Test Results (Y) | 0.79 | 0.71 | 0.82 | 0.82 | 0.73 | 0.77 | 0.72 | 0.79 | 0.72 | 0.91 | Let $\mu_D = \mu_X - \mu_Y$ denote the mean of the differences between X and Y. Test H0: $\mu_D = \mu_X - \mu_Y = 0$ against H1: $\mu_D = \mu_X - \mu_Y > 0$ using t-test for the differences. Let $\alpha = 0.05$. (All values are rounded to the third decimal place.) (Hints: t0.95(9) = 1.833; t0.975(9) = 2.262; t0.95(10) = 1.812; t0.975(10) = 2.228, where P(t < t1-α(r)) = 1 - α for a t random variable with a freedom r)